In an attempt to elucidate the classic violations of expected utility theory, the behavioural economics literature heavily relies on the influential work of Tversky and Kahneman (1992), specifically the Cumulative Prospect Theory (CPT) model and the Heuristics-and-Biases program. While both approaches have significantly contributed to our understanding of decision-making under uncertainty, empirical evidence remains inconclusive. In this study, we investigate the performance of each approach across a wide range of choice environments and increasing cognitive load, encompassing gains, losses, time pressure, and complexity. Utilising data from various studies and employing Bayesian inference, we assess the performance of CPT in comparison to an adaptive cognitive toolbox model of heuristics. For subjects classified as toolbox decision makers, we examine the content (i.e., which heuristics) and the size of the toolbox (i.e., how many heuristics). Our findings reveal that as the choice environment objectively increases in complexity, individuals transition from
using sophisticated expectation-based utility models to relying on a set of simplification heuristics for decision-making. We quantify the relationship between toolbox usage and complexity, showing a significant and positive correlation between the two. Furthermore, our results indicate that as task complexity rises, individuals tend to employ smaller toolboxes with fewer heuristics for decision-making.